Simulation results of highly damped active particles [see Fig. 2(a, b)] show that \(\tau _{ex}\)  is inversely proportional to the self-propulsion length for \(l_\theta << R\) . The opposite limit, \(l_\theta >> R\) , witnesses a linear growth of escape time with \(l_{\theta }\) . In between these two limits, a minimum is observed in \(\tau _{ex}\)  versus \(l_\theta \) . Thus, it appears that different exit mechanisms are involved in the three regimes of \(l_\theta \)  or rotational dynamics. The distinct exit mechanisms can further be anticipated by looking at particle trajectories inside the cavities (see Fig. 1(c)). For \(l_\theta >> \lbrace R, \; l_{th}\rbrace \)  and \(l_{th} <<R\) , our simulations results [see Fig. 1(d-e)] show that particles get accumulated and diffuse along 2D cavity circumference keeping \(\mathbf {v_0}\)  aligned to the position vector \( \mathbf {r}\) . Such type of accumulation of overdamped active particles near boundaries or obstructions is a manifestation of their persistent motions. This feature triggers interesting phenomenologies reported in the earlier studies [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
